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plot_comparison(y_test, y_pred, 'Ordinary Linear Regression, Test Set')
import os
import numpy as np
import scipy.io
from sklearn import linear_model
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score, confusion_matrix, mean_squared_error, r2_score
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
from IPython.display import clear_output
import random
import sys
After reading and preprocessing the data in the next code chunk, the data from all cells is stored in a population dictionary. The dictionary's keys correspond to the cell names, and the values contain the data for each respective cell.
The values in the population dictionary are cell dictionaries with keys being 'axons', 'green_dFFMeanValues',and 'red_dFFMeanValues':
'axons', e.g., cell_data_dict['CL090_230515']['axons'] is a 1 dimensional numpy array, of which the length is the number of groups and the elements are 1 dimensional numpy arrays consisting of components belonging to the group.'green_dFFMeanValues' is a 2 dimensional 3 by 49 numpy array (each cell has 3 rounds, and each round has 8 directions * 2 time frequencies * 3 space frequencies = 48 settings plus a extra period so in total there are 49 columns), of which the elements are still 2 dimensional numpy arrays with size being 10 by N (N is the number of components).'red_dFFMeanValues' is similarly a 2 dimensional 3 by 49 numpy array, of which the elements are still 2 dimensional numpy arrays with size being 10 by 1 (only recording the data at the soma).root_path = "/content/drive/MyDrive/Fluorescence_Data/FluoData4Fitting_Average"
# Get a list of all the subdirectories: subfolders are viewed as cell names
cell_names = [f for f in os.listdir(root_path) if os.path.isdir(os.path.join(root_path, f))]
# for cell in cell_names:
# print(cell)
# Create a dictionary with default values
default_value = 0
cell_data_dict = {cell: default_value for cell in cell_names}
# print(cell_data_dict)
file_suffixes = ['green_Axon.mat', 'green_dFFMeanValues.mat', 'red_dFFMeanValues.mat']
for cell in cell_names:
print(cell)
file_names = [cell + suffix for suffix in file_suffixes]
path_ = file_names[0] # green_Axon.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
axons = mat_data['Axons'] # array containing nested arrays/sub-arrays
# Squeeze the outer array
axons = np.squeeze(axons, axis=0)
for i in range(len(axons)):
# Squeeze the inner array and convert the data type to 'int'
axons[i] = np.squeeze(axons[i].astype(int), axis=0)
# final axons' length is the number of groups with
# each elements being a nested array of components
path_ = file_names[1] # green_dFFMeanValues.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
dFFMeanValues_green = mat_data['dFFMeanValues'] # 3 by 49
path_ = file_names[2] # red_dFFMeanValues.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
dFFMeanValues_red = mat_data['dFFMeanValues'] # 3 by 49
cell_data_dict[cell] = {'axons': axons,
'green_dFFMeanValues': dFFMeanValues_green,
'red_dFFMeanValues': dFFMeanValues_red}
# Print keys and types
for key, value in cell_data_dict.items():
print("-- * * * * * --")
print(key, type(value))
for key_, value_ in value.items():
print(key_, type(value_))
print("-- * * * * * --")
CL090_230515 CL090_230518 CL083_230413 CL075_230303 -- * * * * * -- CL090_230515 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL090_230518 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL083_230413 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL075_230303 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * --
# print to see data type and size
print(cell_data_dict['CL090_230515'].keys())
print(type(cell_data_dict['CL090_230515']['axons']))
print(cell_data_dict['CL090_230515']['axons'].shape)
print(cell_data_dict['CL090_230515']['axons'][1].shape)
print(cell_data_dict['CL090_230515']['axons'][1].dtype)
print("--------------------------------")
print(type(cell_data_dict['CL090_230515']['green_dFFMeanValues']))
print(cell_data_dict['CL090_230515']['green_dFFMeanValues'].shape)
print(type(cell_data_dict['CL090_230515']['green_dFFMeanValues'][1,1]))
print(cell_data_dict['CL090_230515']['green_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['green_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['green_dFFMeanValues'][0,1].dtype)
print("--------------------------------")
print(type(cell_data_dict['CL090_230515']['red_dFFMeanValues']))
print(cell_data_dict['CL090_230515']['red_dFFMeanValues'].shape)
print(type(cell_data_dict['CL090_230515']['red_dFFMeanValues'][1,1]))
print(cell_data_dict['CL090_230515']['red_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['red_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['red_dFFMeanValues'][0,1].dtype)
dict_keys(['axons', 'green_dFFMeanValues', 'red_dFFMeanValues']) <class 'numpy.ndarray'> (25,) (19,) int64 -------------------------------- <class 'numpy.ndarray'> (3, 49) <class 'numpy.ndarray'> (10, 281) (10, 155) float64 -------------------------------- <class 'numpy.ndarray'> (3, 49) <class 'numpy.ndarray'> (10, 1) (10, 2) float64
Note:
Four cells: 'CL090_230515', 'CL090_230518', 'CL083_230413', 'CL075_230303'.
'red_dFFMeanValues' and 'green_dFFMeanValues' have 49 columns,where the last column should be excluded. They are supposed to have 3 rows (3 rounds), but 'CL090_230518' only has 2 rows.
In 'CL083_230413', elements in 'red_dFFMeanValues' have 2 columns (10 × 2， should be 10 × 1), so 'CL083_230413' is not used.
def plot_comparison(y_test, y_pred, subtitle = ''):
# Sort y_pred and y_test based on y_test
sorted_indices = np.argsort(y_test)
sorted_y_pred = y_pred[sorted_indices]
sorted_y_test = y_test[sorted_indices]
# Plot sorted_y_pred and sorted_y_test
plt.plot(sorted_y_pred, label='Sorted Predictions')
plt.plot(sorted_y_test, label='Sorted Ground Truth')
plt.xlabel('Index')
plt.ylabel('Value')
plt.title(f'Comparison of Sorted Predictions and Sorted Ground Truth \n ({subtitle})')
plt.legend()
plt.savefig(f'Comparison ({subtitle}).png', bbox_inches='tight')
# bbox_inches='tight' will adjust the figure's bounding box to fit all the content, ensuring that
# the complete words are visible in the saved figure. Otherwise, the saved figure may not show the
# complete words, e.g., for x-label, or for the long title.
# The default setting can sometimes result in cutoff or clipped text. It tries to include the entire
# figure within the saved image, but there may be cases where the default behavior is not sufficient
# to capture all the content. The default behavior assumes the figure content fits within the predefined
# margins and padding.
plt.show()
cell_data = cell_data_dict['CL090_230515']
# cell_data = cell_data_dict['CL075_230303']
delete_small_group = True # delete groups (axons) with less than 3 components
data_green = cell_data['green_dFFMeanValues'][:,:-1] # exclude 49th column
data_red = cell_data['red_dFFMeanValues'][:,:-1] # exclude 49th column
data_axons = cell_data['axons']
# print(data_axons)
# print(type(data_axons),len(data_axons),data_axons)
if delete_small_group:
data_axons = np.array([axons_ for axons_ in data_axons if len(axons_) >= 3])
# print(type(data_axons),len(data_axons),data_axons)
# vstack green data
stacked_green = np.empty((0, data_green[0,0].shape[1]))
# Enumerate the elements in the np array and vstack them
for index, value in np.ndenumerate(data_green):
stacked_green = np.vstack((stacked_green, value))
print(stacked_green.shape, 48*3*10)
# group columns of green data
group_num = data_axons.shape[0]
group_satcked_green = np.zeros((stacked_green.shape[0], group_num))
for i, cols in enumerate(data_axons):
group_satcked_green[:, i] = np.sum(stacked_green[:, cols-1], axis=1)
print(group_satcked_green.shape, data_axons.shape)
# vstack red data
stacked_red = np.empty((0, data_red[0,0].shape[1]))
# Enumerate the elements in the np array and vstack them
for index, value in np.ndenumerate(data_red):
stacked_red = np.vstack((stacked_red, value))
print(stacked_red.shape, 48*3*10)
print(np.max(group_satcked_green), np.min(group_satcked_green))
print(np.max(stacked_red), np.min(stacked_red))
(1440, 281) 1440 (1440, 23) (23,) (1440, 1) 1440 15.553237533160676 -5.301797778486449 0.6745208147710272 -0.24153973313562027
<ipython-input-70-a898a02bf148>:12: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray. data_axons = np.array([axons_ for axons_ in data_axons if len(axons_) >= 3])
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 23) y_train shape: (1368,) x_test shape: (72, 23) y_test shape: (72,)
Ordinary least squares Linear Regression.
Linear Regression fits a linear model with coefficients to minimize the residual sum of squares between the observed targets in the dataset, and the targets predicted by the linear approximation.
# Create a LinearRegression object
model = linear_model.LinearRegression()
# Fit the model on the training data
model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", model.intercept_)
# Predict on the test data
y_pred = model.predict(x_test)
Fitted Coefficients: [ 0.00858669 0.00743209 0.00014154 -0.00200023 0.00347426 0.00427812 0.00214916 0.02260626 0.00247705 -0.00569123 -0.00090012 0.02778809 0.00892736 -0.00514382 0.00355821 0.00597681 -0.00034941 0.03004997 -0.00226955 0.01099947 -0.03173304 -0.00569335 -0.00660043] Fitted Intercept: -0.004212685462284843
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Mean squared error: 0.008074969164185652 Correlation coefficient: 0.603489712990602 Coefficient of determination (R-squared score, R2 score): 0.3491861509436127
plot_comparison(y_test, y_pred, 'Ordinary Linear Regression, Test Set')
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Mean squared error: 0.006182229460650515 Correlation coefficient: 0.6555470128252661 Coefficient of determination (R-squared score, R2 score): 0.42974188602412944
plot_comparison(y_train, y_pred_, 'Ordinary Linear Regression, Train Set')
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 2.4722222222222223 Correlation coefficient: 0.6337249674698427 Coefficient of determination (R-squared score, R2 score): 0.37296345222369 Mean squared error: 2.040204678362573 Correlation coefficient: 0.6307726975135022 Coefficient of determination (R-squared score, R2 score): 0.39677927369980326
Linear least squares with l2 regularization.
Minimizes the objective function:
$$ ||y - Xw||^2_2 + \alpha ||w||^2_2 $$This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm.
# Create a Ridge Regression object
ridge_model = linear_model.Ridge(alpha=1.0) # You can adjust the value of alpha as per your requirements
# Fit the model on the training data
ridge_model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", ridge_model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", ridge_model.intercept_)
# Predict on the test data
y_pred = ridge_model.predict(x_test)
Fitted Coefficients: [ 0.00858988 0.00743959 0.00011496 -0.00200547 0.00344948 0.00420449 0.00216321 0.0225892 0.00250327 -0.00570704 -0.00097906 0.02775836 0.0089764 -0.00511579 0.0035531 0.00598195 -0.00035286 0.02961701 -0.00223236 0.01091599 -0.03089882 -0.00536224 -0.00594153] Fitted Intercept: -0.004215410911834354
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Ridge Linear Regression, Test Set')
Mean squared error: 0.008074674031217798 Correlation coefficient: 0.6035147326094551 Coefficient of determination (R-squared score, R2 score): 0.34920993761312047
# predict on train
# Use the trained model to make predictions
y_pred_ = ridge_model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Ridge Linear Regression, Train Set')
Mean squared error: 0.006182263250840294 Correlation coefficient: 0.6555447439462398 Coefficient of determination (R-squared score, R2 score): 0.4297387691663652
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 2.4722222222222223 Correlation coefficient: 0.6337249674698427 Coefficient of determination (R-squared score, R2 score): 0.37296345222369 Mean squared error: 2.040204678362573 Correlation coefficient: 0.6307433150910617 Coefficient of determination (R-squared score, R2 score): 0.39677927369980326
Linear regression with combined L1 and L2 priors as regularizer.
Minimizes the objective function:
$$ 1 / (2 * n_{samples}) * ||y - Xw||^2_2 + \alpha * l1_{ratio} * ||w||_1 + 0.5 * \alpha * (1 - l1_{ratio}) * ||w||^2_2 $$If controlling the L1 and L2 penalty separately, that this is equivalent to:
$$ a * ||w||_1 + 0.5 * b * ||w||_2^2 $$where: $\alpha = a + b$ and $l1_{ratio} = a / (a + b)$.
# Create an ElasticNet object
a = 0.004; b = 0.00
alpha = a + b; l1_ratio = a / (a + b)
elasticnet_model = linear_model.ElasticNet(alpha=alpha, l1_ratio=l1_ratio, max_iter=100000)
# adjust the values of alpha and l1_ratio as per your requirements
# Fit the model on the training data
elasticnet_model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", elasticnet_model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", elasticnet_model.intercept_)
# Predict on the test data
y_pred = elasticnet_model.predict(x_test)
# It is normal to encounter warning here, because our data is not linear enough
# and not normailized to guarantee a low error/residual, even though we set a very
# large max_iter. But the results is similar to that of ordinary and Ridge linear
# regression. Like alpha = 0 results in the same results as the ordinary linear
# rergession.
Fitted Coefficients: [ 0.00951724 0.0068485 0. -0. 0.00285676 0. 0. 0.01545406 0.00635406 -0. 0. 0.02601547 0.00529342 -0. 0. 0.00326147 0. 0. 0. 0. -0. 0. 0. ] Fitted Intercept: -0.004587622786060119
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Elasticnet Linear Regression, Test Set')
Mean squared error: 0.008246618904776503 Correlation coefficient: 0.593481482809575 Coefficient of determination (R-squared score, R2 score): 0.33535179119658987
# predict on train
# Use the trained model to make predictions
y_pred_ = elasticnet_model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Elasticnet Linear Regression, Train Set')
Mean squared error: 0.006385274236585692 Correlation coefficient: 0.6428087118878939 Coefficient of determination (R-squared score, R2 score): 0.4110127314829676
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 2.7777777777777777 Correlation coefficient: 0.566099913342907 Coefficient of determination (R-squared score, R2 score): 0.2954645530603258 Mean squared error: 2.1052631578947367 Correlation coefficient: 0.6144590454550366 Coefficient of determination (R-squared score, R2 score): 0.3775436432301804
Mathematically, a power-law relationship can be expressed as:
$$ y = A X^C $$Here, I modify it, shown as:
$$ y = A (X+B)^C + D $$where, $X = \beta_1 x_1 + \beta_2 x_2 \dots + \beta_N x_N$. $X+D$ is a linear regression part. $A$, $B$, $C$, $D$, $\beta_1$, $\beta_2$, ...,$\beta_N$ are parameters to be determined.
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 23) y_train shape: (1368,) x_test shape: (72, 23) y_test shape: (72,)
exponent = 5
# Define the model function
def func(X, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X * np.array(params[3:]), axis=1)
base = weighted_sum + B
power_result = np.power(base, exponent)
return A * power_result + D
# Create a LinearRegression object
model = linear_model.LinearRegression()
# give the initial params using linear regression
# so that the params are within a reasonable range
model.fit(x_train, y_train)
# print("Fitted Coefficients:", model.coef_)
# print("Fitted Intercept:", model.intercept_)
num_features = x_train.shape[1]
# Assuming model.coef_ is the np array containing the coefficients
model_coefs = model.coef_
# Set negative elements to 0 using np.clip()
initial_params = [1, model.intercept_, 0] + list(model_coefs) # Initial parameter guesses
# model_coefs_clipped = np.clip(model_coefs, 0, np.inf)
# initial_params = [1, model.intercept_, 0] + list(model_coefs_clipped) # Initial parameter guesses, no need to clip -- they can be negative
# Set lower and upper bounds for the parameters
lower_bounds = [0, -np.inf, -np.inf] + [0] * num_features
upper_bounds = [np.inf, np.inf, np.inf] + [np.inf] * num_features
# Combine the lower and upper bounds into a 2-tuple of array_like
bounds = (lower_bounds, upper_bounds)
# Perform the curve fit with bounds
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, bounds=bounds, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, B, D = params[:3]
weighted_sum = np.sum(x_test * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent)
y_pred = A * sign * power_result + D
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Power-Law Regression Exponent=5, Test Set')
# predict on train
A, B, D = params[:3]
weighted_sum = np.sum(x_train * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent)
y_pred_ = A * sign * power_result + D
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Power-Law Regression (Exponent=5), Train Set')
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Fitted Parameters: [ 2.77673174e+00 5.43999910e-01 -1.35647651e-01 5.36004086e-03 4.62291296e-03 -4.48053143e-04 -1.51574443e-04 2.89567093e-03 3.50802638e-03 1.95878489e-03 1.43654331e-02 1.08620098e-03 -4.47666558e-03 5.30100512e-04 1.74140339e-02 5.56480031e-03 -4.62509903e-03 1.38103461e-03 3.31131634e-03 -2.81684741e-04 1.90354684e-02 -8.59289923e-03 7.64034998e-03 -2.51367545e-02 -3.33187351e-03 -1.18174866e-02] Mean squared error: 0.007899697746818354 Correlation coefficient: 0.6150864301916624 Coefficient of determination (R-squared score, R2 score): 0.3633124049821176
Mean squared error: 0.0059866374659903725 Correlation coefficient: 0.6691663357118757 Coefficient of determination (R-squared score, R2 score): 0.4477835848471192
---- ---- ---- Mean squared error: 2.513888888888889 Correlation coefficient: 0.6251978930658115 Coefficient of determination (R-squared score, R2 score): 0.36239542051959495 Mean squared error: 1.9400584795321638 Correlation coefficient: 0.6535701067438148 Coefficient of determination (R-squared score, R2 score): 0.4263891767822565
# compared with example 1, here only fit A and D.
exponent = 5
model = linear_model.LinearRegression()
model.fit(x_train, y_train)
# now we have: model.intercept_ and model.coef_
# Print the fitted coefficients
print("Fitted Coefficients:", model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", model.intercept_)
# Define the model function
def func(X, A, D):
# Compute the weighted sum
weighted_sum = np.sum(X * np.array(model.coef_), axis=1)
base = weighted_sum
power_result = np.power(base, exponent)
return A * power_result + D
initial_params = [1, 0]
# Perform the curve fit
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, D = params
y_pred = func(x_test, A, D)
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Power-Law Regression Exponent=5, only fit A and D, Test Set')
# predict on train
A, D = params
y_pred_ = func(x_train, A, D)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Power-Law Regression Exponent=5, only fit A and D, Train Set')
Fitted Coefficients: [ 0.00858669 0.00743209 0.00014154 -0.00200023 0.00347426 0.00427812 0.00214916 0.02260626 0.00247705 -0.00569123 -0.00090012 0.02778809 0.00892736 -0.00514382 0.00355821 0.00597681 -0.00034941 0.03004997 -0.00226955 0.01099947 -0.03173304 -0.00569335 -0.00660043] Fitted Intercept: -0.004212685462284843 Fitted Parameters: [3.27606220e+02 3.68048107e-02] Mean squared error: 0.010328443830817775 Correlation coefficient: 0.4811494140668785 Coefficient of determination (R-squared score, R2 score): 0.1675640924908589
Mean squared error: 0.008925232118984414 Correlation coefficient: 0.42038459588030785 Coefficient of determination (R-squared score, R2 score): 0.1767232084534498
# generate irreducible fraction with an odd number as the denominator
# such numbers can work as the exponent for negative numbers and
# will be used as the parameter "C" in Power-law regression below:
# y = A * (B+b1*x1+b2*x2+...+bN*xN)**C + D
def gcd(a, b): # calculate the greatest common divisor of two numbers
while b:
a, b = b, a % b
return a
def generate_irreducible_fraction(existing_fractions = []):
while True:
numerator = random.randint(1, 400) # Random numerator
denominator = random.randrange(1, 100, 2) # Random odd denominator
if gcd(numerator, denominator) == 1: # Check if the fraction is irreducible
fraction = (numerator, denominator)
if fraction not in existing_fractions: # Check if the fraction is not a duplicate
return fraction
# Generate irreducible fraction numbers
N_faction = 40
upper_bound = 50
irreducible_fractions = []
while len(irreducible_fractions) < N_faction:
fraction = generate_irreducible_fraction(irreducible_fractions)
if fraction[0]/fraction[1] < upper_bound:
irreducible_fractions.append(fraction)
# Sort the irreducible fractions
irreducible_fractions.sort(key=lambda f: f[0] / f[1])
# Print the irreducible fraction numbers
for numerator, denominator in irreducible_fractions:
if random.random() <= 0.1:
print(f"{numerator}/{denominator}")
# Extract the numerator and denominator values
indexes = range(1, len(irreducible_fractions) + 1)
values = [numerator / denominator for numerator, denominator in irreducible_fractions]
# Plot the irreducible fractions
plt.plot(values, 'o-')
plt.xlabel("Index")
plt.ylabel("Irreducible Fraction")
plt.title("Irreducible Fractions")
plt.show()
## if not use the above random generated irreducible_fractions, define it below.
irreducible_fractions = [(1,95), (30,43), (179,65), (5,1), (221,33), (219,23), (300,17), (73,3)]
109/91 55/39 90/43 54/11
# # old code! The new one is in the next chunk.
# params_list = []
# for numerator, denominator in irreducible_fractions:
# C1, C2 = numerator, denominator
# # Define the model function
# def func(X, *params):
# A, B, D = params[:3]
# # Compute the weighted sum
# weighted_sum = np.sum(X * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# return A * sign * power_result + D
# # Create a LinearRegression object
# model = linear_model.LinearRegression()
# # give the initial params using linear regression
# # so that the params are within a reasonable range
# model.fit(x_train, y_train)
# # print("Fitted Coefficients:", model.coef_)
# # print("Fitted Intercept:", model.intercept_)
# num_features = x_train.shape[1]
# initial_params = [1, model.intercept_, 0] + list(model.coef_) # Initial parameter guesses
# # Perform the curve fit
# params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# params_list.append(params)
# # Print the fitted parameters
# # print("Fitted Parameters:", params)
# # predict on test
# y_predict_test_list = []
# for (numerator, denominator), params in zip(irreducible_fractions, params_list):
# C1, C2 = numerator, denominator
# A, B, D = params[:3]
# weighted_sum = np.sum(x_test * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# y_pred = A * sign * power_result + D
# y_predict_test_list.append(y_pred)
# # predict on train
# y_predict_train_list = []
# for (numerator, denominator), params in zip(irreducible_fractions, params_list):
# C1, C2 = numerator, denominator
# A, B, D = params[:3]
# weighted_sum = np.sum(x_train * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# y_pred_ = A * sign * power_result + D
# y_predict_train_list.append(y_pred_)
# new code, a updated version for the code in last chunk.
# input and output data normalization is achieved (but it
# seems normalization is redundant).
class CurveFit_with_Normalization:
def __init__(self, exponent_numerator=1, exponent_denominator=1, input_range=[1,2], output_range=[1,2]):
self.input_min = input_range[0]
self.input_max = input_range[1]
self.output_min = output_range[0]
self.output_max = output_range[1]
self.input_scale = None
self.input_shift = None
self.output_scale = None
self.output_shift = None
self.exponent_numerator = exponent_numerator
self.exponent_denominator = exponent_denominator
self.linear_model = linear_model.LinearRegression()
def fit(self, X, y):
# Normalize the input and output data
self.input_scale = (self.input_max - self.input_min) / (np.max(X) - np.min(X))
self.input_shift = self.input_min - np.min(X) * self.input_scale
normalized_X = self.input_scale * X + self.input_shift
self.output_scale = (self.output_max - self.output_min) / (np.max(y) - np.min(y))
self.output_shift = self.output_min - np.min(y) * self.output_scale
normalized_y = self.output_scale * y + self.output_shift
def normalized_func_(X_normalize, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X_normalize * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, self.exponent_numerator / self.exponent_denominator)
return A * sign * power_result + D
# Give the initial params using linear regression
self.linear_model.fit(normalized_X, normalized_y)
# print("Fitted Coefficients:", linear_model.coef_)
# print("Fitted Intercept:", linear_model.intercept_)
# num_features = X.shape[1]
exponent = self.exponent_numerator / self.exponent_denominator
initial_params = [1, self.linear_model.intercept_ / exponent + (1 - 1 / exponent), 0] + list(self.linear_model.coef_ /
exponent) # Initial parameter guesses
# initial_params = [1, 0, 0] + [1 / X.shape[1]] * (X.shape[1])
# Perform the normalized curve fit
normalized_params, params_covariance = curve_fit(normalized_func_, normalized_X, normalized_y,
p0=initial_params, maxfev=100000000)
# Store the fitted parameters
self.normalized_fitted_params = normalized_params
def predict(self, X):
# Normalize the input data using the previously calculated scaling and shifting parameters
normalized_X = self.input_scale * X + self.input_shift
# Make predictions using the denormalized parameters
y_pred = self.normalized_func(normalized_X, self.exponent_numerator,
self.exponent_denominator, *self.normalized_fitted_params)
# Denormalize the predicted output
y_pred = (y_pred - self.output_shift) / self.output_scale
return y_pred
@staticmethod
def normalized_func(X_normalize, exponent_numerator, exponent_denominator, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X_normalize * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent_numerator / exponent_denominator)
return A * sign * power_result + D
model_list = []
for numerator, denominator in irreducible_fractions:
# Create an instance of NormalizedCurveFit
model = CurveFit_with_Normalization(numerator, denominator, input_range=[1, 2], output_range=[1, 2])
# Fit the model to your input and output data
model.fit(x_train, y_train)
model_list.append(model)
# this is for the new version code in the last chunk
r2_score_test_list = []
# predict on test
y_predict_test_list = []
for model, (numerator, denominator) in zip(model_list, irreducible_fractions):
y_pred = model.predict(x_test)
print(f'-------- \n (numerator, denominator) is: ({numerator}, {denominator})')
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_test_list.append(r_squared)
y_predict_test_list.append(y_pred)
print("|||||||||||||||||||||||||||||||||||||")
r2_score_train_list = []
# predict on train
y_predict_train_list = []
for model, (numerator, denominator) in zip(model_list, irreducible_fractions):
y_pred_ = model.predict(x_train)
print(f'-------- \n (numerator, denominator) is: ({numerator}, {denominator})')
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_train_list.append(r_squared)
y_predict_train_list.append(y_pred_)
x = [numerator / denominator for (numerator, denominator) in irreducible_fractions]
# plot the r2 score curve over exponent
fig, ax = plt.subplots(figsize=(7.5, 5)) # Adjust the values as desired
# Plot the R-squared scores
ax.plot(x, r2_score_train_list, label='Train R-squared')
ax.plot(x, r2_score_test_list, label='Test R-squared')
# Set labels and title with font size
ax.set_xlabel('Exponent in Power Law', fontsize=14)
ax.set_ylabel('R-squared', fontsize=14)
ax.set_title('R-squared Scores', fontsize=16)
# Set tick label font size
ax.tick_params(axis='x', labelsize=12)
ax.tick_params(axis='y', labelsize=12)
# Set legend
ax.legend(fontsize=12)
fig.savefig('Power_Law_r2_scores_plot.png')
# Display the plot
plt.show()
-------- (numerator, denominator) is: (1, 95) Mean squared error: 0.012559302224213718 Correlation coefficient: 0.519175091374801 Coefficient of determination (R-squared score, R2 score): -0.012235174625250256 -------- (numerator, denominator) is: (30, 43) Mean squared error: 0.008075857162392383 Correlation coefficient: 0.603432316751359 Coefficient of determination (R-squared score, R2 score): 0.3491145814404819 -------- (numerator, denominator) is: (179, 65) Mean squared error: 0.00789042898506367 Correlation coefficient: 0.61554643130327 Coefficient of determination (R-squared score, R2 score): 0.3640594342760879 -------- (numerator, denominator) is: (5, 1) Mean squared error: 0.00789966753519557 Correlation coefficient: 0.6150879508419141 Coefficient of determination (R-squared score, R2 score): 0.363314839931665 -------- (numerator, denominator) is: (221, 33) Mean squared error: 0.007902039555052844 Correlation coefficient: 0.6149662659577605 Coefficient of determination (R-squared score, R2 score): 0.3631236635516737 -------- (numerator, denominator) is: (219, 23) Mean squared error: 0.007903925041732525 Correlation coefficient: 0.6148692719396113 Coefficient of determination (R-squared score, R2 score): 0.36297170001863743 -------- (numerator, denominator) is: (300, 17) Mean squared error: 0.007905915171916604 Correlation coefficient: 0.6147643484731915 Coefficient of determination (R-squared score, R2 score): 0.3628113025906239 -------- (numerator, denominator) is: (73, 3) Mean squared error: 0.007906459000763663 Correlation coefficient: 0.6147321777481705 Coefficient of determination (R-squared score, R2 score): 0.3627674719161055 ||||||||||||||||||||||||||||||||||||| -------- (numerator, denominator) is: (1, 95) Mean squared error: 0.010430833328525884 Correlation coefficient: 0.4043584475833738 Coefficient of determination (R-squared score, R2 score): 0.037844295657067595 -------- (numerator, denominator) is: (30, 43) Mean squared error: 0.006182819642508629 Correlation coefficient: 0.6555054909592437 Coefficient of determination (R-squared score, R2 score): 0.42968744676472426 -------- (numerator, denominator) is: (179, 65) Mean squared error: 0.005988448999014988 Correlation coefficient: 0.6690414683527763 Coefficient of determination (R-squared score, R2 score): 0.44761648632504114 -------- (numerator, denominator) is: (5, 1) Mean squared error: 0.005986637464351129 Correlation coefficient: 0.6691663358228005 Coefficient of determination (R-squared score, R2 score): 0.4477835849983255 -------- (numerator, denominator) is: (221, 33) Mean squared error: 0.005986523567234973 Correlation coefficient: 0.6691741858898774 Coefficient of determination (R-squared score, R2 score): 0.44779409103907664 -------- (numerator, denominator) is: (219, 23) Mean squared error: 0.0059865089423562536 Correlation coefficient: 0.6691751940651628 Coefficient of determination (R-squared score, R2 score): 0.44779544005981564 -------- (numerator, denominator) is: (300, 17) Mean squared error: 0.0059865570371726105 Correlation coefficient: 0.6691718794557059 Coefficient of determination (R-squared score, R2 score): 0.4477910037218501 -------- (numerator, denominator) is: (73, 3) Mean squared error: 0.005986583486160919 Correlation coefficient: 0.6691700561356378 Coefficient of determination (R-squared score, R2 score): 0.44778856402751577
# for model in model_list:
# print(model.exponent_numerator, model.exponent_denominator)
# both the old and new versions (in the last subsection "Fit and predict") of code
# share the same evaluate code in this subsectoon.
# Create and update multiple figures (test)
for y_pred, (numerator, denominator) in zip(y_predict_test_list, irreducible_fractions):
plot_comparison(y_test, y_pred, f'Power-Law Regression Exponent={numerator} over {denominator}, Test Set')
# here pay attention: cannot use / replace over in the name, otherwise cannot save the fig
# because / cannot be in a file name.
print(y_pred[0])
clear_output(wait=True) # Clear the previous output
0.018717463150803165
# Create and update multiple figures (train)
for y_pred_, (numerator, denominator) in zip(y_predict_train_list, irreducible_fractions):
plot_comparison(y_train, y_pred_, f'Power-Law Regression Exponent={numerator} over {denominator}, Train Set')
print(y_pred_[0])
clear_output(wait=True) # Clear the previous output
0.09086895719690612
Let $B = (b_1, b_2, \ldots , b_N)$. $$ y = A \cdot e^{(b_1 \cdot x_1 + \ldots + b_N \cdot x_N)} + C $$
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 23) y_train shape: (1368,) x_test shape: (72, 23) y_test shape: (72,)
# Define the model function
def func(X, *params):
A, C = params[:2]
return A * np.exp(np.sum(X * np.array(params[2:]), axis=1)) + C
# give the initial params using linear regression
# so that the params are within a reasonable range
num_features = x_train.shape[1]
initial_params = [np.mean(y_train), 0] + [0] * num_features # Initial parameter guesses
# Perform the curve fit
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, C = params[:2]
y_pred = A * np.exp(np.sum(x_test * np.array(params[2:]), axis=1)) + C
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
# predict on train
A, C = params[:2]
y_pred_ = A * np.exp(np.sum(x_train * np.array(params[2:]), axis=1)) + C
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_train_list.append(r_squared)
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
print(y_pred)
print(y_pred_test_digital)
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Fitted Parameters: [ 0.1823746 -0.18536285 0.03597331 0.0307567 -0.00330851 -0.00091631 0.01954615 0.02318797 0.01372602 0.09625164 0.00709798 -0.02993611 0.00246999 0.11763575 0.03731833 -0.03118017 0.00842956 0.02293895 -0.00277306 0.12789089 -0.05908822 0.05215503 -0.16760929 -0.02179579 -0.07699066] Mean squared error: 0.007908076477834208 Correlation coefficient: 0.6146448099384035 Coefficient of determination (R-squared score, R2 score): 0.3626371090061502 Mean squared error: 0.005986673289208099 Correlation coefficient: 0.6691638666723004 Coefficient of determination (R-squared score, R2 score): 0.4477802804598092 ---- ---- ---- [ 0.01875636 0.15397279 0.12609907 0.06998503 0.04392775 0.21967305 -0.01277599 0.14068255 0.08104014 0.21846992 -0.0073211 0.05619991 -0.01621427 0.02825998 -0.05298555 -0.01625067 -0.05514395 0.11258016 0.09896961 0.00616822 0.04468552 0.13469012 0.01325329 0.05852102 0.01324546 0.06602263 0.07967526 0.02230262 0.03634778 0.10003435 -0.02892226 -0.01719065 0.16842691 -0.00762978 0.05009483 -0.03333179 0.29598064 0.00354518 0.06034039 -0.01651624 -0.03354982 0.0544459 0.06747314 0.06040705 0.0163658 -0.01422737 0.15947881 0.19936708 0.02348646 0.02492627 0.04168845 0.0420574 0.03511103 0.08387374 0.01295184 0.09199935 0.04017838 -0.08793826 0.18409705 -0.02652792 -0.01010585 0.02097629 0.02614643 0.00104492 0.09725656 -0.01098192 -0.0099172 0.11324766 0.03823631 -0.01320243 0.08362394 0.05546906] [4 6 6 5 4 8 3 6 5 8 4 5 3 4 3 3 3 6 5 4 4 6 4 5 4 5 5 4 4 5 3 3 7 4 5 3 9 4 5 3 3 5 5 5 4 3 7 7 4 4 4 4 4 5 4 5 4 2 7 3 4 4 4 4 5 4 4 6 4 3 5 5] Mean squared error: 2.513888888888889 Correlation coefficient: 0.6251978930658115 Coefficient of determination (R-squared score, R2 score): 0.36239542051959495 Mean squared error: 1.9437134502923976 Correlation coefficient: 0.6527532920188056 Coefficient of determination (R-squared score, R2 score): 0.42530852338508673
plot_comparison(y_test, y_pred, 'Exponential Regression, Test Set')
plot_comparison(y_train, y_pred_, 'Exponential Regression, Train Set')
# independent data
x = group_satcked_green
class_num = 480
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# print(np.max(y), np.min(y))
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
x_train shape: (1368, 23) y_train shape: (1368,) x_test shape: (72, 23) y_test shape: (72,) Unique elements: [ 0 7 27 36 38 40 43 50 52 54 55 56 57 58 60 61 62 63 65 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 210 211 212 213 214 215 216 217 218 219 220 222 223 224 226 227 228 229 230 231 232 233 234 235 237 238 240 242 243 244 245 246 247 250 251 253 254 255 256 257 258 259 260 263 265 266 267 268 269 270 272 273 274 277 280 283 285 286 287 288 290 291 293 294 300 310 311 315 322 323 326 327 329 332 334 335 336 339 340 343 349 356 357 360 369 380 383 389 391 426 475 479] Number of unique elements: 253
'multinomial' (default option for multi-calss) achieves better performance than 'ovr'.
# fit
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='multinomial')
# model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='ovr')
fit_result = model.fit(x_train, y_train)
print(fit_result.intercept_.shape, fit_result.coef_.shape)
# print("Coefficients:", model.coef_[0,:])
# print("Intercept:", model.intercept_[0])
print('--- --- ---')
# predict
# Use the trained model to make predictions
y_pred = model.predict(x_test)
# Alternatively, you can get the predicted probabilities for each class
y_prob = model.predict_proba(x_test)
print('y_prob.shape:', y_prob.shape)
print(np.sum(y_prob, axis = 1))
# print(y_prob[0,:])
# Print the predicted class labels
print('y_pred:', y_pred)
print('y_test:', y_test)
print('y_pred shape:', y_pred.shape, 'y_test shape:', y_test.shape)
# Print the predicted probabilities
# print(y_prob)
(253,) (253, 23) --- --- --- y_prob.shape: (72, 253) [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] y_pred: [122 168 182 158 129 293 132 244 223 291 122 161 110 108 132 84 78 138 211 145 131 199 116 129 130 184 163 137 165 153 141 126 188 113 148 75 327 166 131 117 108 134 120 124 132 141 184 211 196 127 130 138 97 144 134 129 126 103 183 145 123 135 145 106 162 145 119 171 138 122 184 170] y_test: [195 131 252 352 130 217 105 183 176 281 157 180 79 165 107 86 109 128 254 299 149 219 127 161 115 160 139 143 97 185 152 134 189 128 113 101 306 160 142 122 122 124 300 124 124 137 176 282 115 178 99 150 117 151 160 222 189 108 179 76 189 112 120 93 150 136 85 221 170 118 160 163] y_pred shape: (72,) y_test shape: (72,)
In previous data division, I classify data into class_num (e.g., class_num = 160) intervals (histogram, by np.digitize). Here, evaluate the results with the same number of classes (e.g., class_num = 160).
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
# cm = confusion_matrix(y_test, y_pred)
# print("Confusion Matrix:") # y_test doesn't include all classes, so confusion matrix is less than num_class by num_class
# print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
# Sort y_pred and y_test based on y_test
plot_comparison(y_test, y_pred, 'Logistic Linear Regression, Test Set')
Accuracy: 0.013888888888888888 Mean squared error: 2563.9444444444443 Correlation coefficient: 0.5661491222250555 Coefficient of determination (R-squared score, R2 score): 0.24678329168154234
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
# Alternatively, you can get the predicted probabilities for each class
y_prob_ = model.predict_proba(x_train)
accuracy = accuracy_score(y_train, y_pred_)
print("Accuracy:", accuracy)
# cm = confusion_matrix(y_train, y_pred_)
# print("Confusion Matrix:")
# print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Logistic Linear Regression, Train Set')
Accuracy: 0.23538011695906433 Mean squared error: 1430.1345029239767 Correlation coefficient: 0.7554692735579654 Coefficient of determination (R-squared score, R2 score): 0.5193623267069408
The model is based on classifying data into class_num (e.g., class_num = 160) intervals (histogram, by np.digitize). Here, evaluate the results a smaller number of classes (e.g., reduced_class_num = 16), that is, for the example of class_num = 160 and reduced_class_num = 16, classes 0, 1, ..., 15 become one class, i.e., 0; ...; classes 144, 145, ..., 159 become one class, i.e., 15.
print("---- ---- ----")
# Define the boundaries for digitization
reduced_class_num = 16
intervals = np.arange(0, class_num + 1, class_num / reduced_class_num)
print(intervals)
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
print(y_pred)
print(y_pred_test_digital)
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- [ 0. 30. 60. 90. 120. 150. 180. 210. 240. 270. 300. 330. 360. 390. 420. 450. 480.] [122 168 182 158 129 293 132 244 223 291 122 161 110 108 132 84 78 138 211 145 131 199 116 129 130 184 163 137 165 153 141 126 188 113 148 75 327 166 131 117 108 134 120 124 132 141 184 211 196 127 130 138 97 144 134 129 126 103 183 145 123 135 145 106 162 145 119 171 138 122 184 170] [ 4 5 6 5 4 9 4 8 7 9 4 5 3 3 4 2 2 4 7 4 4 6 3 4 4 6 5 4 5 5 4 4 6 3 4 2 10 5 4 3 3 4 4 4 4 4 6 7 6 4 4 4 3 4 4 4 4 3 6 4 4 4 4 3 5 4 3 5 4 4 6 5] Mean squared error: 2.7222222222222223 Correlation coefficient: 0.6060794440849583 Coefficient of determination (R-squared score, R2 score): 0.3095552619991193 Mean squared error: 1.7185672514619883 Correlation coefficient: 0.7430224939475898 Coefficient of determination (R-squared score, R2 score): 0.4918767726507479
Fixing the reduced class number, I enumerate the original class number to see what a original class number is better.
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
reduced_class_num = 16
class_num_array = np.arange(reduced_class_num, reduced_class_num * 100 + 1, reduced_class_num)
# class_num_array = np.arange(reduced_class_num * 5, reduced_class_num * 40 + 1, reduced_class_num)
mse_test_list = []
correlation_test_list = []
r_squared_test_list = []
mse_train_list = []
correlation_train_list = []
r_squared_train_list = []
for class_num in class_num_array:
print('---- ---- ----')
print(f'class_num = {class_num}')
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
# print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='multinomial')
fit_result = model.fit(x_train, y_train)
y_pred = model.predict(x_test)
y_pred_ = model.predict(x_train)
# Define the boundaries for digitization
intervals = np.arange(0, class_num+1, class_num/16)
print(intervals)
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
# print(y_pred)
# print(y_pred_test_digital)
print("test eval:")
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse_test_list.append(mse)
correlation_test_list.append(correlation)
r_squared_test_list.append(r_squared)
print("train eval:")
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse_train_list.append(mse)
correlation_train_list.append(correlation)
r_squared_train_list.append(r_squared)
plot_comparison(y_test, y_pred, f'Logistic Linear Regression Reduced Evaluation {class_num} to {reduced_class_num}, Test Set')
plot_comparison(y_train, y_pred_, f'Logistic Linear Regression Reduced Evaluation {class_num} to {reduced_class_num}, Train Set')
x_train shape: (1368, 23) y_train shape: (1368,) x_test shape: (72, 23) y_test shape: (72,) ---- ---- ---- class_num = 16 Number of unique elements: 16 [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.] test eval: Mean squared error: 3.638888888888889 Correlation coefficient: 0.4687928259791623 Coefficient of determination (R-squared score, R2 score): 0.07705856450902682 train eval: Mean squared error: 2.3077485380116958 Correlation coefficient: 0.5888470929409589 Coefficient of determination (R-squared score, R2 score): 0.3176754450269721
---- ---- ---- class_num = 32 Number of unique elements: 29 [ 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32.] test eval: Mean squared error: 3.1527777777777777 Correlation coefficient: 0.5487438273703586 Coefficient of determination (R-squared score, R2 score): 0.2003522677234698 train eval: Mean squared error: 2.2112573099415203 Correlation coefficient: 0.6184086486227316 Coefficient of determination (R-squared score, R2 score): 0.34620469471225546
---- ---- ---- class_num = 48 Number of unique elements: 40 [ 0. 3. 6. 9. 12. 15. 18. 21. 24. 27. 30. 33. 36. 39. 42. 45. 48.] test eval: Mean squared error: 3.4166666666666665 Correlation coefficient: 0.49941168671042274 Coefficient of determination (R-squared score, R2 score): 0.1334214002642008 train eval: Mean squared error: 2.236842105263158 Correlation coefficient: 0.6163107352143256 Coefficient of determination (R-squared score, R2 score): 0.33864012093206664
---- ---- ---- class_num = 64 Number of unique elements: 54 [ 0. 4. 8. 12. 16. 20. 24. 28. 32. 36. 40. 44. 48. 52. 56. 60. 64.] test eval: Mean squared error: 3.4166666666666665 Correlation coefficient: 0.5026790965894902 Coefficient of determination (R-squared score, R2 score): 0.1334214002642008 train eval: Mean squared error: 2.1140350877192984 Correlation coefficient: 0.6472779452398354 Coefficient of determination (R-squared score, R2 score): 0.37495007507697287
---- ---- ---- class_num = 80 Number of unique elements: 64 [ 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. 55. 60. 65. 70. 75. 80.] test eval: Mean squared error: 4.180555555555555 Correlation coefficient: 0.4427520028671864 Coefficient of determination (R-squared score, R2 score): -0.060325847644209674 train eval: Mean squared error: 2.2353801169590644 Correlation coefficient: 0.6346212091961099 Coefficient of determination (R-squared score, R2 score): 0.3390723822909346
---- ---- ---- class_num = 96 Number of unique elements: 71 [ 0. 6. 12. 18. 24. 30. 36. 42. 48. 54. 60. 66. 72. 78. 84. 90. 96.] test eval: Mean squared error: 3.2916666666666665 Correlation coefficient: 0.51125505041414 Coefficient of determination (R-squared score, R2 score): 0.16512549537648613 train eval: Mean squared error: 2.1783625730994154 Correlation coefficient: 0.6520909781713446 Coefficient of determination (R-squared score, R2 score): 0.35593057528678385
---- ---- ---- class_num = 112 Number of unique elements: 84 [ 0. 7. 14. 21. 28. 35. 42. 49. 56. 63. 70. 77. 84. 91. 98. 105. 112.] test eval: Mean squared error: 3.513888888888889 Correlation coefficient: 0.4939418406770864 Coefficient of determination (R-squared score, R2 score): 0.10876265962131215 train eval: Mean squared error: 2.1922514619883042 Correlation coefficient: 0.6486678241151259 Coefficient of determination (R-squared score, R2 score): 0.35182409237753853
---- ---- ---- class_num = 128 Number of unique elements: 94 [ 0. 8. 16. 24. 32. 40. 48. 56. 64. 72. 80. 88. 96. 104. 112. 120. 128.] test eval: Mean squared error: 3.4444444444444446 Correlation coefficient: 0.49173742109172 Coefficient of determination (R-squared score, R2 score): 0.1263760457948041 train eval: Mean squared error: 1.9619883040935673 Correlation coefficient: 0.6884820898799331 Coefficient of determination (R-squared score, R2 score): 0.4199052563992376
---- ---- ---- class_num = 144 Number of unique elements: 103 [ 0. 9. 18. 27. 36. 45. 54. 63. 72. 81. 90. 99. 108. 117. 126. 135. 144.] test eval: Mean squared error: 3.4722222222222223 Correlation coefficient: 0.5038498771736062 Coefficient of determination (R-squared score, R2 score): 0.1193306913254073 train eval: Mean squared error: 2.081140350877193 Correlation coefficient: 0.6704811540011679 Coefficient of determination (R-squared score, R2 score): 0.38467595565150126
---- ---- ---- class_num = 160 Number of unique elements: 112 [ 0. 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120. 130. 140. 150. 160.] test eval: Mean squared error: 3.2916666666666665 Correlation coefficient: 0.5242259606046868 Coefficient of determination (R-squared score, R2 score): 0.16512549537648613 train eval: Mean squared error: 2.122076023391813 Correlation coefficient: 0.6703961059512124 Coefficient of determination (R-squared score, R2 score): 0.37257263760319925
---- ---- ---- class_num = 176 Number of unique elements: 119 [ 0. 11. 22. 33. 44. 55. 66. 77. 88. 99. 110. 121. 132. 143. 154. 165. 176.] test eval: Mean squared error: 3.0694444444444446 Correlation coefficient: 0.5449911491568233 Coefficient of determination (R-squared score, R2 score): 0.2214883311316601 train eval: Mean squared error: 1.8888888888888888 Correlation coefficient: 0.701823124253286 Coefficient of determination (R-squared score, R2 score): 0.44151832434263405
---- ---- ---- class_num = 192 Number of unique elements: 129 [ 0. 12. 24. 36. 48. 60. 72. 84. 96. 108. 120. 132. 144. 156. 168. 180. 192.] test eval: Mean squared error: 2.9305555555555554 Correlation coefficient: 0.5666814362142001 Coefficient of determination (R-squared score, R2 score): 0.2567151034786438 train eval: Mean squared error: 2.0701754385964914 Correlation coefficient: 0.6798531086562069 Coefficient of determination (R-squared score, R2 score): 0.3879179158430107
---- ---- ---- class_num = 208 Number of unique elements: 135 [ 0. 13. 26. 39. 52. 65. 78. 91. 104. 117. 130. 143. 156. 169. 182. 195. 208.] test eval: Mean squared error: 3.236111111111111 Correlation coefficient: 0.5199406664337747 Coefficient of determination (R-squared score, R2 score): 0.17921620431527963 train eval: Mean squared error: 1.972953216374269 Correlation coefficient: 0.6981366843232758 Coefficient of determination (R-squared score, R2 score): 0.41666329620772813
---- ---- ---- class_num = 224 Number of unique elements: 144 [ 0. 14. 28. 42. 56. 70. 84. 98. 112. 126. 140. 154. 168. 182. 196. 210. 224.] test eval: Mean squared error: 3.2083333333333335 Correlation coefficient: 0.5494219764429203 Coefficient of determination (R-squared score, R2 score): 0.18626155878467632 train eval: Mean squared error: 2.0285087719298245 Correlation coefficient: 0.6943943636148544 Coefficient of determination (R-squared score, R2 score): 0.40023736457074677
---- ---- ---- class_num = 240 Number of unique elements: 151 [ 0. 15. 30. 45. 60. 75. 90. 105. 120. 135. 150. 165. 180. 195. 210. 225. 240.] test eval: Mean squared error: 3.2916666666666665 Correlation coefficient: 0.5194551289734144 Coefficient of determination (R-squared score, R2 score): 0.16512549537648613 train eval: Mean squared error: 2.068713450292398 Correlation coefficient: 0.6870658969529513 Coefficient of determination (R-squared score, R2 score): 0.3883501772018787
---- ---- ---- class_num = 256 Number of unique elements: 162 [ 0. 16. 32. 48. 64. 80. 96. 112. 128. 144. 160. 176. 192. 208. 224. 240. 256.] test eval: Mean squared error: 3.361111111111111 Correlation coefficient: 0.5009248047595136 Coefficient of determination (R-squared score, R2 score): 0.1475121092029943 train eval: Mean squared error: 1.8735380116959064 Correlation coefficient: 0.711584492903241 Coefficient of determination (R-squared score, R2 score): 0.44605706861074734
---- ---- ---- class_num = 272 Number of unique elements: 168 [ 0. 17. 34. 51. 68. 85. 102. 119. 136. 153. 170. 187. 204. 221. 238. 255. 272.] test eval: Mean squared error: 3.5277777777777777 Correlation coefficient: 0.48355826570450633 Coefficient of determination (R-squared score, R2 score): 0.1052399823866138 train eval: Mean squared error: 1.837719298245614 Correlation coefficient: 0.7243368869370695 Coefficient of determination (R-squared score, R2 score): 0.4566474719030117
---- ---- ---- class_num = 288 Number of unique elements: 174 [ 0. 18. 36. 54. 72. 90. 108. 126. 144. 162. 180. 198. 216. 234. 252. 270. 288.] test eval: Mean squared error: 3.5416666666666665 Correlation coefficient: 0.4909596921609652 Coefficient of determination (R-squared score, R2 score): 0.10171730515191546 train eval: Mean squared error: 2.0116959064327484 Correlation coefficient: 0.6872185719452775 Coefficient of determination (R-squared score, R2 score): 0.40520837019772793
---- ---- ---- class_num = 304 Number of unique elements: 184 [ 0. 19. 38. 57. 76. 95. 114. 133. 152. 171. 190. 209. 228. 247. 266. 285. 304.] test eval: Mean squared error: 3.0694444444444446 Correlation coefficient: 0.5466411991576089 Coefficient of determination (R-squared score, R2 score): 0.2214883311316601 train eval: Mean squared error: 1.9064327485380117 Correlation coefficient: 0.7069074436555871 Coefficient of determination (R-squared score, R2 score): 0.43633118803621895
---- ---- ---- class_num = 320 Number of unique elements: 191 [ 0. 20. 40. 60. 80. 100. 120. 140. 160. 180. 200. 220. 240. 260. 280. 300. 320.] test eval: Mean squared error: 3.4583333333333335 Correlation coefficient: 0.4860162880041063 Coefficient of determination (R-squared score, R2 score): 0.12285336856010565 train eval: Mean squared error: 2.0555555555555554 Correlation coefficient: 0.6960384889149112 Coefficient of determination (R-squared score, R2 score): 0.3922405294316901
---- ---- ---- class_num = 336 Number of unique elements: 197 [ 0. 21. 42. 63. 84. 105. 126. 147. 168. 189. 210. 231. 252. 273. 294. 315. 336.] test eval: Mean squared error: 3.875 Correlation coefficient: 0.4401436050735745 Coefficient of determination (R-squared score, R2 score): 0.017173051519154603 train eval: Mean squared error: 1.8033625730994152 Correlation coefficient: 0.7273991259341729 Coefficient of determination (R-squared score, R2 score): 0.46680561383640795
---- ---- ---- class_num = 352 Number of unique elements: 205 [ 0. 22. 44. 66. 88. 110. 132. 154. 176. 198. 220. 242. 264. 286. 308. 330. 352.] test eval: Mean squared error: 3.361111111111111 Correlation coefficient: 0.5037429919980371 Coefficient of determination (R-squared score, R2 score): 0.1475121092029943 train eval: Mean squared error: 1.7690058479532165 Correlation coefficient: 0.7299640096335394 Coefficient of determination (R-squared score, R2 score): 0.4769637557698043
---- ---- ---- class_num = 368 Number of unique elements: 212 [ 0. 23. 46. 69. 92. 115. 138. 161. 184. 207. 230. 253. 276. 299. 322. 345. 368.] test eval: Mean squared error: 3.125 Correlation coefficient: 0.5332746426444116 Coefficient of determination (R-squared score, R2 score): 0.20739762219286662 train eval: Mean squared error: 1.9663742690058479 Correlation coefficient: 0.6957804399311407 Coefficient of determination (R-squared score, R2 score): 0.41860847232263376
---- ---- ---- class_num = 384 Number of unique elements: 219 [ 0. 24. 48. 72. 96. 120. 144. 168. 192. 216. 240. 264. 288. 312. 336. 360. 384.] test eval: Mean squared error: 3.4722222222222223 Correlation coefficient: 0.5059495216654009 Coefficient of determination (R-squared score, R2 score): 0.1193306913254073 train eval: Mean squared error: 1.6513157894736843 Correlation coefficient: 0.7533710508112701 Coefficient of determination (R-squared score, R2 score): 0.5117607951586727
---- ---- ---- class_num = 400 Number of unique elements: 224 [ 0. 25. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 300. 325. 350. 375. 400.] test eval: Mean squared error: 3.5277777777777777 Correlation coefficient: 0.4977597173786398 Coefficient of determination (R-squared score, R2 score): 0.1052399823866138 train eval: Mean squared error: 1.608187134502924 Correlation coefficient: 0.7559141771554772 Coefficient of determination (R-squared score, R2 score): 0.5245125052452767
---- ---- ---- class_num = 416 Number of unique elements: 226 [ 0. 26. 52. 78. 104. 130. 156. 182. 208. 234. 260. 286. 312. 338. 364. 390. 416.] test eval: Mean squared error: 3.388888888888889 Correlation coefficient: 0.4852968909152171 Coefficient of determination (R-squared score, R2 score): 0.1404667547335975 train eval: Mean squared error: 1.7105263157894737 Correlation coefficient: 0.7473274313076835 Coefficient of determination (R-squared score, R2 score): 0.49425421012452153
---- ---- ---- class_num = 432 Number of unique elements: 234 [ 0. 27. 54. 81. 108. 135. 162. 189. 216. 243. 270. 297. 324. 351. 378. 405. 432.] test eval: Mean squared error: 3.6944444444444446 Correlation coefficient: 0.4654611943310215 Coefficient of determination (R-squared score, R2 score): 0.06296785557023332 train eval: Mean squared error: 1.8757309941520468 Correlation coefficient: 0.7169540141364958 Coefficient of determination (R-squared score, R2 score): 0.44540867657244543
---- ---- ---- class_num = 448 Number of unique elements: 243 [ 0. 28. 56. 84. 112. 140. 168. 196. 224. 252. 280. 308. 336. 364. 392. 420. 448.] test eval: Mean squared error: 3.125 Correlation coefficient: 0.5148756853854868 Coefficient of determination (R-squared score, R2 score): 0.20739762219286662 train eval: Mean squared error: 1.8004385964912282 Correlation coefficient: 0.7354031088299798 Coefficient of determination (R-squared score, R2 score): 0.4676701365541439
---- ---- ---- class_num = 464 Number of unique elements: 243 [ 0. 29. 58. 87. 116. 145. 174. 203. 232. 261. 290. 319. 348. 377. 406. 435. 464.] test eval: Mean squared error: 3.013888888888889 Correlation coefficient: 0.5562252199875786 Coefficient of determination (R-squared score, R2 score): 0.2355790400704535 train eval: Mean squared error: 1.7236842105263157 Correlation coefficient: 0.7436713273369112 Coefficient of determination (R-squared score, R2 score): 0.49036385789471015
---- ---- ---- class_num = 480 Number of unique elements: 253 [ 0. 30. 60. 90. 120. 150. 180. 210. 240. 270. 300. 330. 360. 390. 420. 450. 480.] test eval: Mean squared error: 2.7222222222222223 Correlation coefficient: 0.6060794440849583 Coefficient of determination (R-squared score, R2 score): 0.3095552619991193 train eval: Mean squared error: 1.7185672514619883 Correlation coefficient: 0.7430224939475898 Coefficient of determination (R-squared score, R2 score): 0.4918767726507479
---- ---- ---- class_num = 496 Number of unique elements: 257 [ 0. 31. 62. 93. 124. 155. 186. 217. 248. 279. 310. 341. 372. 403. 434. 465. 496.] test eval: Mean squared error: 3.5 Correlation coefficient: 0.4832186801513632 Coefficient of determination (R-squared score, R2 score): 0.11228533685601061 train eval: Mean squared error: 1.7046783625730995 Correlation coefficient: 0.7407108544490708 Coefficient of determination (R-squared score, R2 score): 0.49598325555999334
---- ---- ---- class_num = 512 Number of unique elements: 265 [ 0. 32. 64. 96. 128. 160. 192. 224. 256. 288. 320. 352. 384. 416. 448. 480. 512.] test eval: Mean squared error: 3.4166666666666665 Correlation coefficient: 0.4900594619824944 Coefficient of determination (R-squared score, R2 score): 0.1334214002642008 train eval: Mean squared error: 1.638157894736842 Correlation coefficient: 0.7544240186941623 Coefficient of determination (R-squared score, R2 score): 0.5156511473884842
---- ---- ---- class_num = 528 Number of unique elements: 270 [ 0. 33. 66. 99. 132. 165. 198. 231. 264. 297. 330. 363. 396. 429. 462. 495. 528.] test eval: Mean squared error: 4.027777777777778 Correlation coefficient: 0.43736758254217567 Coefficient of determination (R-squared score, R2 score): -0.021576398062527424 train eval: Mean squared error: 1.7653508771929824 Correlation coefficient: 0.7341467667031194 Coefficient of determination (R-squared score, R2 score): 0.4780444091669742
---- ---- ---- class_num = 544 Number of unique elements: 277 [ 0. 34. 68. 102. 136. 170. 204. 238. 272. 306. 340. 374. 408. 442. 476. 510. 544.] test eval: Mean squared error: 4.0 Correlation coefficient: 0.4100064508731889 Coefficient of determination (R-squared score, R2 score): -0.014531043593130732 train eval: Mean squared error: 1.5285087719298245 Correlation coefficient: 0.7712613048121688 Coefficient of determination (R-squared score, R2 score): 0.5480707493035789
---- ---- ---- class_num = 560 Number of unique elements: 277 [ 0. 35. 70. 105. 140. 175. 210. 245. 280. 315. 350. 385. 420. 455. 490. 525. 560.] test eval: Mean squared error: 3.9166666666666665 Correlation coefficient: 0.47230871755082143 Coefficient of determination (R-squared score, R2 score): 0.006605019815059454 train eval: Mean squared error: 1.5957602339181287 Correlation coefficient: 0.7585438890414924 Coefficient of determination (R-squared score, R2 score): 0.5281867267956541
---- ---- ---- class_num = 576 Number of unique elements: 286 [ 0. 36. 72. 108. 144. 180. 216. 252. 288. 324. 360. 396. 432. 468. 504. 540. 576.] test eval: Mean squared error: 3.9722222222222223 Correlation coefficient: 0.42378310656099694 Coefficient of determination (R-squared score, R2 score): -0.007485689123734041 train eval: Mean squared error: 1.668859649122807 Correlation coefficient: 0.7486151433385978 Coefficient of determination (R-squared score, R2 score): 0.5065736588522576
---- ---- ---- class_num = 592 Number of unique elements: 292 [ 0. 37. 74. 111. 148. 185. 222. 259. 296. 333. 370. 407. 444. 481. 518. 555. 592.] test eval: Mean squared error: 3.388888888888889 Correlation coefficient: 0.49399417848482213 Coefficient of determination (R-squared score, R2 score): 0.1404667547335975 train eval: Mean squared error: 1.6527777777777777 Correlation coefficient: 0.7482079193849351 Coefficient of determination (R-squared score, R2 score): 0.5113285337998048
---- ---- ---- class_num = 608 Number of unique elements: 300 [ 0. 38. 76. 114. 152. 190. 228. 266. 304. 342. 380. 418. 456. 494. 532. 570. 608.] test eval: Mean squared error: 2.861111111111111 Correlation coefficient: 0.5654923211396736 Coefficient of determination (R-squared score, R2 score): 0.27432848965213563 train eval: Mean squared error: 1.4846491228070176 Correlation coefficient: 0.7759283496987173 Coefficient of determination (R-squared score, R2 score): 0.5610385900696169
---- ---- ---- class_num = 624 Number of unique elements: 304 [ 0. 39. 78. 117. 156. 195. 234. 273. 312. 351. 390. 429. 468. 507. 546. 585. 624.] test eval: Mean squared error: 3.6666666666666665 Correlation coefficient: 0.41626635730762723 Coefficient of determination (R-squared score, R2 score): 0.07001321003963012 train eval: Mean squared error: 1.5416666666666667 Correlation coefficient: 0.7635377869560491 Coefficient of determination (R-squared score, R2 score): 0.5441803970737675
---- ---- ---- class_num = 640 Number of unique elements: 307 [ 0. 40. 80. 120. 160. 200. 240. 280. 320. 360. 400. 440. 480. 520. 560. 600. 640.] test eval: Mean squared error: 3.4305555555555554 Correlation coefficient: 0.4839848288307079 Coefficient of determination (R-squared score, R2 score): 0.12989872302950245 train eval: Mean squared error: 1.6030701754385965 Correlation coefficient: 0.7605854385805896 Coefficient of determination (R-squared score, R2 score): 0.5260254200013145
---- ---- ---- class_num = 656 Number of unique elements: 309 [ 0. 41. 82. 123. 164. 205. 246. 287. 328. 369. 410. 451. 492. 533. 574. 615. 656.] test eval: Mean squared error: 3.8055555555555554 Correlation coefficient: 0.37497588643165786 Coefficient of determination (R-squared score, R2 score): 0.034786437692646444 train eval: Mean squared error: 1.543859649122807 Correlation coefficient: 0.7655178452810798 Coefficient of determination (R-squared score, R2 score): 0.5435320050354656
---- ---- ---- class_num = 672 Number of unique elements: 315 [ 0. 42. 84. 126. 168. 210. 252. 294. 336. 378. 420. 462. 504. 546. 588. 630. 672.] test eval: Mean squared error: 3.1666666666666665 Correlation coefficient: 0.5150190255186106 Coefficient of determination (R-squared score, R2 score): 0.19682959048877147 train eval: Mean squared error: 1.554093567251462 Correlation coefficient: 0.7633699426681166 Coefficient of determination (R-squared score, R2 score): 0.5405061755233902
---- ---- ---- class_num = 688 Number of unique elements: 321 [ 0. 43. 86. 129. 172. 215. 258. 301. 344. 387. 430. 473. 516. 559. 602. 645. 688.] test eval: Mean squared error: 4.013888888888889 Correlation coefficient: 0.4005119454382824 Coefficient of determination (R-squared score, R2 score): -0.01805372082782908 train eval: Mean squared error: 1.5526315789473684 Correlation coefficient: 0.772042638034626 Coefficient of determination (R-squared score, R2 score): 0.5409384368822581
---- ---- ---- class_num = 704 Number of unique elements: 332 [ 0. 44. 88. 132. 176. 220. 264. 308. 352. 396. 440. 484. 528. 572. 616. 660. 704.] test eval: Mean squared error: 3.763888888888889 Correlation coefficient: 0.43791853374799544 Coefficient of determination (R-squared score, R2 score): 0.04535446939674148 train eval: Mean squared error: 1.4371345029239766 Correlation coefficient: 0.7840847983118878 Coefficient of determination (R-squared score, R2 score): 0.5750870842328246
---- ---- ---- class_num = 720 Number of unique elements: 327 [ 0. 45. 90. 135. 180. 225. 270. 315. 360. 405. 450. 495. 540. 585. 630. 675. 720.] test eval: Mean squared error: 3.486111111111111 Correlation coefficient: 0.4555483337428381 Coefficient of determination (R-squared score, R2 score): 0.11580801409070896 train eval: Mean squared error: 1.519736842105263 Correlation coefficient: 0.7710688567836358 Coefficient of determination (R-squared score, R2 score): 0.5506643174567865
---- ---- ---- class_num = 736 Number of unique elements: 337 [ 0. 46. 92. 138. 184. 230. 276. 322. 368. 414. 460. 506. 552. 598. 644. 690. 736.] test eval: Mean squared error: 4.375 Correlation coefficient: 0.3886319421222251 Coefficient of determination (R-squared score, R2 score): -0.10964332892998674 train eval: Mean squared error: 1.6695906432748537 Correlation coefficient: 0.7500292249655928 Coefficient of determination (R-squared score, R2 score): 0.5063575281728236
---- ---- ---- class_num = 752 Number of unique elements: 342 [ 0. 47. 94. 141. 188. 235. 282. 329. 376. 423. 470. 517. 564. 611. 658. 705. 752.] test eval: Mean squared error: 3.861111111111111 Correlation coefficient: 0.4226049614507438 Coefficient of determination (R-squared score, R2 score): 0.02069572875385295 train eval: Mean squared error: 1.5204678362573099 Correlation coefficient: 0.7693164965472329 Coefficient of determination (R-squared score, R2 score): 0.5504481867773525
---- ---- ---- class_num = 768 Number of unique elements: 355 [ 0. 48. 96. 144. 192. 240. 288. 336. 384. 432. 480. 528. 576. 624. 672. 720. 768.] test eval: Mean squared error: 3.5555555555555554 Correlation coefficient: 0.4702633221611583 Coefficient of determination (R-squared score, R2 score): 0.09819462791721711 train eval: Mean squared error: 1.4663742690058479 Correlation coefficient: 0.7787359072431008 Coefficient of determination (R-squared score, R2 score): 0.5664418570554659
---- ---- ---- class_num = 784 Number of unique elements: 351 [ 0. 49. 98. 147. 196. 245. 294. 343. 392. 441. 490. 539. 588. 637. 686. 735. 784.] test eval: Mean squared error: 3.2916666666666665 Correlation coefficient: 0.4910675336428644 Coefficient of determination (R-squared score, R2 score): 0.16512549537648613 train eval: Mean squared error: 1.4722222222222223 Correlation coefficient: 0.781659838703789 Coefficient of determination (R-squared score, R2 score): 0.5647128116199942
---- ---- ---- class_num = 800 Number of unique elements: 355 [ 0. 50. 100. 150. 200. 250. 300. 350. 400. 450. 500. 550. 600. 650. 700. 750. 800.] test eval: Mean squared error: 3.8333333333333335 Correlation coefficient: 0.4353159979326409 Coefficient of determination (R-squared score, R2 score): 0.02774108322324964 train eval: Mean squared error: 1.5394736842105263 Correlation coefficient: 0.7663863922881011 Coefficient of determination (R-squared score, R2 score): 0.5448287891120694
---- ---- ---- class_num = 816 Number of unique elements: 365 [ 0. 51. 102. 153. 204. 255. 306. 357. 408. 459. 510. 561. 612. 663. 714. 765. 816.] test eval: Mean squared error: 3.25 Correlation coefficient: 0.5351553225029251 Coefficient of determination (R-squared score, R2 score): 0.17569352708058128 train eval: Mean squared error: 1.4349415204678362 Correlation coefficient: 0.7826942834897845 Coefficient of determination (R-squared score, R2 score): 0.5757354762711264
---- ---- ---- class_num = 832 Number of unique elements: 369 [ 0. 52. 104. 156. 208. 260. 312. 364. 416. 468. 520. 572. 624. 676. 728. 780. 832.] test eval: Mean squared error: 3.1944444444444446 Correlation coefficient: 0.5262219237468545 Coefficient of determination (R-squared score, R2 score): 0.18978423601937477 train eval: Mean squared error: 1.388157894736842 Correlation coefficient: 0.7929796795446294 Coefficient of determination (R-squared score, R2 score): 0.5895678397549002
---- ---- ---- class_num = 848 Number of unique elements: 374 [ 0. 53. 106. 159. 212. 265. 318. 371. 424. 477. 530. 583. 636. 689. 742. 795. 848.] test eval: Mean squared error: 3.2916666666666665 Correlation coefficient: 0.48057246999800624 Coefficient of determination (R-squared score, R2 score): 0.16512549537648613 train eval: Mean squared error: 1.4144736842105263 Correlation coefficient: 0.7874109795102556 Coefficient of determination (R-squared score, R2 score): 0.5817871352952775
---- ---- ---- class_num = 864 Number of unique elements: 376 [ 0. 54. 108. 162. 216. 270. 324. 378. 432. 486. 540. 594. 648. 702. 756. 810. 864.] test eval: Mean squared error: 3.9027777777777777 Correlation coefficient: 0.3868950782276027 Coefficient of determination (R-squared score, R2 score): 0.0101276970497578 train eval: Mean squared error: 1.3888888888888888 Correlation coefficient: 0.7899206380480293 Coefficient of determination (R-squared score, R2 score): 0.5893517090754663
---- ---- ---- class_num = 880 Number of unique elements: 375 [ 0. 55. 110. 165. 220. 275. 330. 385. 440. 495. 550. 605. 660. 715. 770. 825. 880.] test eval: Mean squared error: 3.486111111111111 Correlation coefficient: 0.49164609130152154 Coefficient of determination (R-squared score, R2 score): 0.11580801409070896 train eval: Mean squared error: 1.4583333333333333 Correlation coefficient: 0.7816575550944759 Coefficient of determination (R-squared score, R2 score): 0.5688192945292396
---- ---- ---- class_num = 896 Number of unique elements: 388 [ 0. 56. 112. 168. 224. 280. 336. 392. 448. 504. 560. 616. 672. 728. 784. 840. 896.] test eval: Mean squared error: 3.3333333333333335 Correlation coefficient: 0.5034573464200038 Coefficient of determination (R-squared score, R2 score): 0.15455746367239098 train eval: Mean squared error: 1.418859649122807 Correlation coefficient: 0.7842767491979115 Coefficient of determination (R-squared score, R2 score): 0.5804903512186737
---- ---- ---- class_num = 912 Number of unique elements: 393 [ 0. 57. 114. 171. 228. 285. 342. 399. 456. 513. 570. 627. 684. 741. 798. 855. 912.] test eval: Mean squared error: 4.097222222222222 Correlation coefficient: 0.4141246013159934 Coefficient of determination (R-squared score, R2 score): -0.039189784236019376 train eval: Mean squared error: 1.3589181286549707 Correlation coefficient: 0.7941628504978642 Coefficient of determination (R-squared score, R2 score): 0.5982130669322587
---- ---- ---- class_num = 928 Number of unique elements: 393 [ 0. 58. 116. 174. 232. 290. 348. 406. 464. 522. 580. 638. 696. 754. 812. 870. 928.] test eval: Mean squared error: 3.0277777777777777 Correlation coefficient: 0.5306120337926347 Coefficient of determination (R-squared score, R2 score): 0.23205636283575515 train eval: Mean squared error: 1.3662280701754386 Correlation coefficient: 0.7924892184466998 Coefficient of determination (R-squared score, R2 score): 0.5960517601379192
---- ---- ---- class_num = 944 Number of unique elements: 398 [ 0. 59. 118. 177. 236. 295. 354. 413. 472. 531. 590. 649. 708. 767. 826. 885. 944.] test eval: Mean squared error: 3.2777777777777777 Correlation coefficient: 0.5038584858703183 Coefficient of determination (R-squared score, R2 score): 0.16864817261118448 train eval: Mean squared error: 1.3801169590643274 Correlation coefficient: 0.7907728953927907 Coefficient of determination (R-squared score, R2 score): 0.5919452772286737
---- ---- ---- class_num = 960 Number of unique elements: 398 [ 0. 60. 120. 180. 240. 300. 360. 420. 480. 540. 600. 660. 720. 780. 840. 900. 960.] test eval: Mean squared error: 3.4305555555555554 Correlation coefficient: 0.4767013049209689 Coefficient of determination (R-squared score, R2 score): 0.12989872302950245 train eval: Mean squared error: 1.3567251461988303 Correlation coefficient: 0.7948123485707044 Coefficient of determination (R-squared score, R2 score): 0.5988614589705608
---- ---- ---- class_num = 976 Number of unique elements: 408 [ 0. 61. 122. 183. 244. 305. 366. 427. 488. 549. 610. 671. 732. 793. 854. 915. 976.] test eval: Mean squared error: 3.986111111111111 Correlation coefficient: 0.46251262770571977 Coefficient of determination (R-squared score, R2 score): -0.011008366358432387 train eval: Mean squared error: 1.4042397660818713 Correlation coefficient: 0.7902669648816 Coefficient of determination (R-squared score, R2 score): 0.584812964807353
---- ---- ---- class_num = 992 Number of unique elements: 406 [ 0. 62. 124. 186. 248. 310. 372. 434. 496. 558. 620. 682. 744. 806. 868. 930. 992.] test eval: Mean squared error: 4.25 Correlation coefficient: 0.4169227166945107 Coefficient of determination (R-squared score, R2 score): -0.0779392338177014 train eval: Mean squared error: 1.3969298245614035 Correlation coefficient: 0.7885553217191804 Coefficient of determination (R-squared score, R2 score): 0.5869742716016926
---- ---- ---- class_num = 1008 Number of unique elements: 414 [ 0. 63. 126. 189. 252. 315. 378. 441. 504. 567. 630. 693. 756. 819. 882. 945. 1008.] test eval: Mean squared error: 4.055555555555555 Correlation coefficient: 0.4171084530480764 Coefficient of determination (R-squared score, R2 score): -0.028621752531924338 train eval: Mean squared error: 1.3954678362573099 Correlation coefficient: 0.7909628141996667 Coefficient of determination (R-squared score, R2 score): 0.5874065329605606
---- ---- ---- class_num = 1024 Number of unique elements: 421 [ 0. 64. 128. 192. 256. 320. 384. 448. 512. 576. 640. 704. 768. 832. 896. 960. 1024.] test eval: Mean squared error: 4.097222222222222 Correlation coefficient: 0.369574849704913 Coefficient of determination (R-squared score, R2 score): -0.039189784236019376 train eval: Mean squared error: 1.3216374269005848 Correlation coefficient: 0.7993317759207863 Coefficient of determination (R-squared score, R2 score): 0.609235731583391
---- ---- ---- class_num = 1040 Number of unique elements: 429 [ 0. 65. 130. 195. 260. 325. 390. 455. 520. 585. 650. 715. 780. 845. 910. 975. 1040.] test eval: Mean squared error: 4.222222222222222 Correlation coefficient: 0.38461444972865816 Coefficient of determination (R-squared score, R2 score): -0.07089387934830471 train eval: Mean squared error: 1.4429824561403508 Correlation coefficient: 0.7833282616354201 Coefficient of determination (R-squared score, R2 score): 0.5733580387973528
---- ---- ---- class_num = 1056 Number of unique elements: 428 [ 0. 66. 132. 198. 264. 330. 396. 462. 528. 594. 660. 726. 792. 858. 924. 990. 1056.] test eval: Mean squared error: 3.4166666666666665 Correlation coefficient: 0.49316794072568415 Coefficient of determination (R-squared score, R2 score): 0.1334214002642008 train eval: Mean squared error: 1.314327485380117 Correlation coefficient: 0.8030066187698501 Coefficient of determination (R-squared score, R2 score): 0.6113970383777307
---- ---- ---- class_num = 1072 Number of unique elements: 435 [ 0. 67. 134. 201. 268. 335. 402. 469. 536. 603. 670. 737. 804. 871. 938. 1005. 1072.] test eval: Mean squared error: 3.4722222222222223 Correlation coefficient: 0.497773439480096 Coefficient of determination (R-squared score, R2 score): 0.1193306913254073 train eval: Mean squared error: 1.2244152046783625 Correlation coefficient: 0.8166071499634825 Coefficient of determination (R-squared score, R2 score): 0.6379811119481085
---- ---- ---- class_num = 1088 Number of unique elements: 437 [ 0. 68. 136. 204. 272. 340. 408. 476. 544. 612. 680. 748. 816. 884. 952. 1020. 1088.] test eval: Mean squared error: 3.6527777777777777 Correlation coefficient: 0.45987763081270244 Coefficient of determination (R-squared score, R2 score): 0.07353588727432847 train eval: Mean squared error: 1.3019005847953216 Correlation coefficient: 0.8065959356445227 Coefficient of determination (R-squared score, R2 score): 0.6150712599281081
---- ---- ---- class_num = 1104 Number of unique elements: 435 [ 0. 69. 138. 207. 276. 345. 414. 483. 552. 621. 690. 759. 828. 897. 966. 1035. 1104.] test eval: Mean squared error: 4.125 Correlation coefficient: 0.3830549835135723 Coefficient of determination (R-squared score, R2 score): -0.04623513870541607 train eval: Mean squared error: 1.280701754385965 Correlation coefficient: 0.8080829464036917 Coefficient of determination (R-squared score, R2 score): 0.6213390496316931
---- ---- ---- class_num = 1120 Number of unique elements: 443 [ 0. 70. 140. 210. 280. 350. 420. 490. 560. 630. 700. 770. 840. 910. 980. 1050. 1120.] test eval: Mean squared error: 4.625 Correlation coefficient: 0.36213763845889224 Coefficient of determination (R-squared score, R2 score): -0.1730515191545574 train eval: Mean squared error: 1.2046783625730995 Correlation coefficient: 0.8191018992346507 Coefficient of determination (R-squared score, R2 score): 0.6438166402928254
---- ---- ---- class_num = 1136 Number of unique elements: 446 [ 0. 71. 142. 213. 284. 355. 426. 497. 568. 639. 710. 781. 852. 923. 994. 1065. 1136.] test eval: Mean squared error: 3.763888888888889 Correlation coefficient: 0.452082055121772 Coefficient of determination (R-squared score, R2 score): 0.04535446939674148 train eval: Mean squared error: 1.2273391812865497 Correlation coefficient: 0.8177558150890845 Coefficient of determination (R-squared score, R2 score): 0.6371165892303725
---- ---- ---- class_num = 1152 Number of unique elements: 453 [ 0. 72. 144. 216. 288. 360. 432. 504. 576. 648. 720. 792. 864. 936. 1008. 1080. 1152.] test eval: Mean squared error: 3.3055555555555554 Correlation coefficient: 0.5030456830970099 Coefficient of determination (R-squared score, R2 score): 0.16160281814178779 train eval: Mean squared error: 1.2543859649122806 Correlation coefficient: 0.8129471611031277 Coefficient of determination (R-squared score, R2 score): 0.6291197540913158
---- ---- ---- class_num = 1168 Number of unique elements: 463 [ 0. 73. 146. 219. 292. 365. 438. 511. 584. 657. 730. 803. 876. 949. 1022. 1095. 1168.] test eval: Mean squared error: 3.763888888888889 Correlation coefficient: 0.41847194394248616 Coefficient of determination (R-squared score, R2 score): 0.04535446939674148 train eval: Mean squared error: 1.1564327485380117 Correlation coefficient: 0.8292765652047343 Coefficient of determination (R-squared score, R2 score): 0.6580812651354672
---- ---- ---- class_num = 1184 Number of unique elements: 457 [ 0. 74. 148. 222. 296. 370. 444. 518. 592. 666. 740. 814. 888. 962. 1036. 1110. 1184.] test eval: Mean squared error: 3.5694444444444446 Correlation coefficient: 0.4536007210378372 Coefficient of determination (R-squared score, R2 score): 0.09467195068251877 train eval: Mean squared error: 1.2682748538011697 Correlation coefficient: 0.8115310279797219 Coefficient of determination (R-squared score, R2 score): 0.6250132711820705
---- ---- ---- class_num = 1200 Number of unique elements: 464 [ 0. 75. 150. 225. 300. 375. 450. 525. 600. 675. 750. 825. 900. 975. 1050. 1125. 1200.] test eval: Mean squared error: 3.8055555555555554 Correlation coefficient: 0.39485006534468375 Coefficient of determination (R-squared score, R2 score): 0.034786437692646444 train eval: Mean squared error: 1.1966374269005848 Correlation coefficient: 0.8167581826335334 Coefficient of determination (R-squared score, R2 score): 0.6461940777665991
---- ---- ---- class_num = 1216 Number of unique elements: 476 [ 0. 76. 152. 228. 304. 380. 456. 532. 608. 684. 760. 836. 912. 988. 1064. 1140. 1216.] test eval: Mean squared error: 3.9166666666666665 Correlation coefficient: 0.347297234354348 Coefficient of determination (R-squared score, R2 score): 0.006605019815059454 train eval: Mean squared error: 1.0994152046783625 Correlation coefficient: 0.8346613117121789 Coefficient of determination (R-squared score, R2 score): 0.6749394581313164
---- ---- ---- class_num = 1232 Number of unique elements: 480 [ 0. 77. 154. 231. 308. 385. 462. 539. 616. 693. 770. 847. 924. 1001. 1078. 1155. 1232.] test eval: Mean squared error: 3.4305555555555554 Correlation coefficient: 0.49179006421871096 Coefficient of determination (R-squared score, R2 score): 0.12989872302950245 train eval: Mean squared error: 1.1980994152046784 Correlation coefficient: 0.8208287473137247 Coefficient of determination (R-squared score, R2 score): 0.6457618164077311
---- ---- ---- class_num = 1248 Number of unique elements: 474 [ 0. 78. 156. 234. 312. 390. 468. 546. 624. 702. 780. 858. 936. 1014. 1092. 1170. 1248.] test eval: Mean squared error: 3.1805555555555554 Correlation coefficient: 0.5440613383250746 Coefficient of determination (R-squared score, R2 score): 0.19330691325407312 train eval: Mean squared error: 1.1703216374269005 Correlation coefficient: 0.8237467664827569 Coefficient of determination (R-squared score, R2 score): 0.6539747822262219
---- ---- ---- class_num = 1264 Number of unique elements: 487 [ 0. 79. 158. 237. 316. 395. 474. 553. 632. 711. 790. 869. 948. 1027. 1106. 1185. 1264.] test eval: Mean squared error: 3.625 Correlation coefficient: 0.44557698347128855 Coefficient of determination (R-squared score, R2 score): 0.08058124174372527 train eval: Mean squared error: 1.0460526315789473 Correlation coefficient: 0.8425111589922274 Coefficient of determination (R-squared score, R2 score): 0.6907169977299958
---- ---- ---- class_num = 1280 Number of unique elements: 488 [ 0. 80. 160. 240. 320. 400. 480. 560. 640. 720. 800. 880. 960. 1040. 1120. 1200. 1280.] test eval: Mean squared error: 3.736111111111111 Correlation coefficient: 0.4095466365789959 Coefficient of determination (R-squared score, R2 score): 0.052399823866138284 train eval: Mean squared error: 1.1359649122807018 Correlation coefficient: 0.8329563015533834 Coefficient of determination (R-squared score, R2 score): 0.6641329241596181
---- ---- ---- class_num = 1296 Number of unique elements: 492 [ 0. 81. 162. 243. 324. 405. 486. 567. 648. 729. 810. 891. 972. 1053. 1134. 1215. 1296.] test eval: Mean squared error: 3.7916666666666665 Correlation coefficient: 0.42597061673103304 Coefficient of determination (R-squared score, R2 score): 0.03830911492734479 train eval: Mean squared error: 1.0738304093567252 Correlation coefficient: 0.8365987896759114 Coefficient of determination (R-squared score, R2 score): 0.6825040319115052
---- ---- ---- class_num = 1312 Number of unique elements: 499 [ 0. 82. 164. 246. 328. 410. 492. 574. 656. 738. 820. 902. 984. 1066. 1148. 1230. 1312.] test eval: Mean squared error: 3.4722222222222223 Correlation coefficient: 0.46263440199102385 Coefficient of determination (R-squared score, R2 score): 0.1193306913254073 train eval: Mean squared error: 1.0285087719298245 Correlation coefficient: 0.8446545225524482 Coefficient of determination (R-squared score, R2 score): 0.695904134036411
---- ---- ---- class_num = 1328 Number of unique elements: 497 [ 0. 83. 166. 249. 332. 415. 498. 581. 664. 747. 830. 913. 996. 1079. 1162. 1245. 1328.] test eval: Mean squared error: 4.180555555555555 Correlation coefficient: 0.3639564680255573 Coefficient of determination (R-squared score, R2 score): -0.060325847644209674 train eval: Mean squared error: 1.0972222222222223 Correlation coefficient: 0.8354458647351714 Coefficient of determination (R-squared score, R2 score): 0.6755878501696183
---- ---- ---- class_num = 1344 Number of unique elements: 501 [ 0. 84. 168. 252. 336. 420. 504. 588. 672. 756. 840. 924. 1008. 1092. 1176. 1260. 1344.] test eval: Mean squared error: 3.5555555555555554 Correlation coefficient: 0.4278885631510579 Coefficient of determination (R-squared score, R2 score): 0.09819462791721711 train eval: Mean squared error: 1.1535087719298245 Correlation coefficient: 0.8274173135311866 Coefficient of determination (R-squared score, R2 score): 0.658945787853203
---- ---- ---- class_num = 1360 Number of unique elements: 503 [ 0. 85. 170. 255. 340. 425. 510. 595. 680. 765. 850. 935. 1020. 1105. 1190. 1275. 1360.] test eval: Mean squared error: 3.4444444444444446 Correlation coefficient: 0.4750872969502953 Coefficient of determination (R-squared score, R2 score): 0.1263760457948041 train eval: Mean squared error: 1.1454678362573099 Correlation coefficient: 0.8292980782943642 Coefficient of determination (R-squared score, R2 score): 0.6613232253269766
---- ---- ---- class_num = 1376 Number of unique elements: 511 [ 0. 86. 172. 258. 344. 430. 516. 602. 688. 774. 860. 946. 1032. 1118. 1204. 1290. 1376.] test eval: Mean squared error: 3.986111111111111 Correlation coefficient: 0.344048389033826 Coefficient of determination (R-squared score, R2 score): -0.011008366358432387 train eval: Mean squared error: 1.0635964912280702 Correlation coefficient: 0.839118031259084 Coefficient of determination (R-squared score, R2 score): 0.6855298614235807
---- ---- ---- class_num = 1392 Number of unique elements: 519 [ 0. 87. 174. 261. 348. 435. 522. 609. 696. 783. 870. 957. 1044. 1131. 1218. 1305. 1392.] test eval: Mean squared error: 4.027777777777778 Correlation coefficient: 0.3611800633782349 Coefficient of determination (R-squared score, R2 score): -0.021576398062527424 train eval: Mean squared error: 1.0804093567251463 Correlation coefficient: 0.8372478144071908 Coefficient of determination (R-squared score, R2 score): 0.6805588557965996
---- ---- ---- class_num = 1408 Number of unique elements: 510 [ 0. 88. 176. 264. 352. 440. 528. 616. 704. 792. 880. 968. 1056. 1144. 1232. 1320. 1408.] test eval: Mean squared error: 4.444444444444445 Correlation coefficient: 0.32220575105907284 Coefficient of determination (R-squared score, R2 score): -0.1272567151034787 train eval: Mean squared error: 1.1396198830409356 Correlation coefficient: 0.8293762709229742 Coefficient of determination (R-squared score, R2 score): 0.6630522707624483
---- ---- ---- class_num = 1424 Number of unique elements: 523 [ 0. 89. 178. 267. 356. 445. 534. 623. 712. 801. 890. 979. 1068. 1157. 1246. 1335. 1424.] test eval: Mean squared error: 3.8055555555555554 Correlation coefficient: 0.37666407530779566 Coefficient of determination (R-squared score, R2 score): 0.034786437692646444 train eval: Mean squared error: 1.111842105263158 Correlation coefficient: 0.8326718022984398 Coefficient of determination (R-squared score, R2 score): 0.6712652365809391
---- ---- ---- class_num = 1440 Number of unique elements: 519 [ 0. 90. 180. 270. 360. 450. 540. 630. 720. 810. 900. 990. 1080. 1170. 1260. 1350. 1440.] test eval: Mean squared error: 3.8333333333333335 Correlation coefficient: 0.3990012392632226 Coefficient of determination (R-squared score, R2 score): 0.02774108322324964 train eval: Mean squared error: 1.159356725146199 Correlation coefficient: 0.8268538540769912 Coefficient of determination (R-squared score, R2 score): 0.6572167424177313
---- ---- ---- class_num = 1456 Number of unique elements: 530 [ 0. 91. 182. 273. 364. 455. 546. 637. 728. 819. 910. 1001. 1092. 1183. 1274. 1365. 1456.] test eval: Mean squared error: 3.486111111111111 Correlation coefficient: 0.46288158551816044 Coefficient of determination (R-squared score, R2 score): 0.11580801409070896 train eval: Mean squared error: 1.1206140350877194 Correlation coefficient: 0.832788863279217 Coefficient of determination (R-squared score, R2 score): 0.6686716684277314
---- ---- ---- class_num = 1472 Number of unique elements: 525 [ 0. 92. 184. 276. 368. 460. 552. 644. 736. 828. 920. 1012. 1104. 1196. 1288. 1380. 1472.] test eval: Mean squared error: 4.333333333333333 Correlation coefficient: 0.35037505674205355 Coefficient of determination (R-squared score, R2 score): -0.0990752972258917 train eval: Mean squared error: 1.1279239766081872 Correlation coefficient: 0.8316401718962996 Coefficient of determination (R-squared score, R2 score): 0.6665103616333918
---- ---- ---- class_num = 1488 Number of unique elements: 532 [ 0. 93. 186. 279. 372. 465. 558. 651. 744. 837. 930. 1023. 1116. 1209. 1302. 1395. 1488.] test eval: Mean squared error: 3.9027777777777777 Correlation coefficient: 0.3973386098897478 Coefficient of determination (R-squared score, R2 score): 0.0101276970497578 train eval: Mean squared error: 0.9941520467836257 Correlation coefficient: 0.8501895373823004 Coefficient of determination (R-squared score, R2 score): 0.7060622759698074
---- ---- ---- class_num = 1504 Number of unique elements: 534 [ 0. 94. 188. 282. 376. 470. 564. 658. 752. 846. 940. 1034. 1128. 1222. 1316. 1410. 1504.] test eval: Mean squared error: 3.7777777777777777 Correlation coefficient: 0.3976083689307804 Coefficient of determination (R-squared score, R2 score): 0.041831792162043135 train eval: Mean squared error: 1.0730994152046784 Correlation coefficient: 0.8408354592901018 Coefficient of determination (R-squared score, R2 score): 0.6827201625909392
---- ---- ---- class_num = 1520 Number of unique elements: 538 [ 0. 95. 190. 285. 380. 475. 570. 665. 760. 855. 950. 1045. 1140. 1235. 1330. 1425. 1520.] test eval: Mean squared error: 3.736111111111111 Correlation coefficient: 0.4395767950620604 Coefficient of determination (R-squared score, R2 score): 0.052399823866138284 train eval: Mean squared error: 0.9985380116959064 Correlation coefficient: 0.8490027388673501 Coefficient of determination (R-squared score, R2 score): 0.7047654918932036
---- ---- ---- class_num = 1536 Number of unique elements: 543 [ 0. 96. 192. 288. 384. 480. 576. 672. 768. 864. 960. 1056. 1152. 1248. 1344. 1440. 1536.] test eval: Mean squared error: 4.347222222222222 Correlation coefficient: 0.3112322889339678 Coefficient of determination (R-squared score, R2 score): -0.10259797446059005 train eval: Mean squared error: 0.9349415204678363 Correlation coefficient: 0.8588087876125522 Coefficient of determination (R-squared score, R2 score): 0.7235688610039586
---- ---- ---- class_num = 1552 Number of unique elements: 552 [ 0. 97. 194. 291. 388. 485. 582. 679. 776. 873. 970. 1067. 1164. 1261. 1358. 1455. 1552.] test eval: Mean squared error: 4.916666666666667 Correlation coefficient: 0.3376522863225631 Coefficient of determination (R-squared score, R2 score): -0.24702774108322334 train eval: Mean squared error: 1.182748538011696 Correlation coefficient: 0.8272127868310696 Coefficient of determination (R-squared score, R2 score): 0.6503005606758444
---- ---- ---- class_num = 1568 Number of unique elements: 546 [ 0. 98. 196. 294. 392. 490. 588. 686. 784. 882. 980. 1078. 1176. 1274. 1372. 1470. 1568.] test eval: Mean squared error: 3.8333333333333335 Correlation coefficient: 0.36276795113160476 Coefficient of determination (R-squared score, R2 score): 0.02774108322324964 train eval: Mean squared error: 1.131578947368421 Correlation coefficient: 0.8309722430137153 Coefficient of determination (R-squared score, R2 score): 0.6654297082362219
---- ---- ---- class_num = 1584 Number of unique elements: 553 [ 0. 99. 198. 297. 396. 495. 594. 693. 792. 891. 990. 1089. 1188. 1287. 1386. 1485. 1584.] test eval: Mean squared error: 3.75 Correlation coefficient: 0.4037425622438564 Coefficient of determination (R-squared score, R2 score): 0.04887714663143994 train eval: Mean squared error: 1.0635964912280702 Correlation coefficient: 0.8402518880823773 Coefficient of determination (R-squared score, R2 score): 0.6855298614235807
---- ---- ---- class_num = 1600 Number of unique elements: 554 [ 0. 100. 200. 300. 400. 500. 600. 700. 800. 900. 1000. 1100. 1200. 1300. 1400. 1500. 1600.] test eval: Mean squared error: 3.8055555555555554 Correlation coefficient: 0.3784207614719348 Coefficient of determination (R-squared score, R2 score): 0.034786437692646444 train eval: Mean squared error: 1.0730994152046784 Correlation coefficient: 0.8394382861035301 Coefficient of determination (R-squared score, R2 score): 0.6827201625909392
# plot the trend figures of mse, correlation, and r2
# Create a figure and subplots
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(8, 12))
# Plot MSE
ax1.plot(class_num_array, mse_test_list, label='MSE (Test)')
ax1.plot(class_num_array, mse_train_list, label='MSE (Train)')
ax1.set_ylabel('MSE')
ax1.set_xlabel('Original Class Number')
ax1.set_title(f'MSE Curve (reduced class num is {reduced_class_num})')
ax1.legend()
# Plot Correlation
ax2.plot(class_num_array, correlation_test_list, label='Correlation (Test)')
ax2.plot(class_num_array, correlation_train_list, label='Correlation (Train)')
ax2.set_ylabel('Correlation')
ax2.set_xlabel('Original Class Number')
ax2.set_title(f'Correlation Curve (reduced class num is {reduced_class_num})')
ax2.legend()
# Plot R-squared
ax3.plot(class_num_array, r_squared_test_list, label='R-squared (Test)')
ax3.plot(class_num_array, r_squared_train_list, label='R-squared (Train)')
ax3.set_ylabel('R-squared')
ax3.set_xlabel('Original Class Number')
ax3.set_title(f'R-squared Curve (reduced class num is {reduced_class_num})')
ax3.legend()
# Increase the vertical spacing between subplots
plt.subplots_adjust(hspace=0.5)
# Adjust tick, label, title, and legend font sizes
plt.rcParams.update({'font.size': 12})
ax1.tick_params(labelsize=10)
ax2.tick_params(labelsize=10)
ax3.tick_params(labelsize=10)
# Save the figure
plt.savefig(f'mse_correlation_r2_trend_curve_reduced_eval_reduced_class_num_{reduced_class_num}.png', bbox_inches='tight')
# Show the figure
plt.show()
# Convert r_squared_test_list to a NumPy array
r_squared_test_array = np.array(r_squared_test_list)
# Find the index of the maximum value
max_index = np.argmax(r_squared_test_array)
# Get the corresponding class_num value
max_class_num = class_num_array[max_index]
# Print the index and corresponding class_num
print("Max Index:", max_index)
print("Max Original Class Num:", max_class_num)
Max Index: 29 Max Original Class Num: 480
balanced weights don't improve the fitting, but make it worse.
# independent data
x = group_satcked_green
class_num = 48
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# print(np.max(y), np.min(y))
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
x_train shape: (1368, 23) y_train shape: (1368,) x_test shape: (72, 23) y_test shape: (72,) Unique elements: [ 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38 39 42 47] Number of unique elements: 40
# fit
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, class_weight='balanced', multi_class='multinomial')
fit_result = model.fit(x_train, y_train)
print(fit_result.intercept_.shape, fit_result.coef_.shape)
# predict
# Use the trained model to make predictions
y_pred = model.predict(x_test)
# Alternatively, you can get the predicted probabilities for each class
y_prob = model.predict_proba(x_test)
# Print the predicted class labels
print(y_pred, y_test)
print(y_pred.shape, y_test.shape)
# Print the predicted probabilities
# print(y_prob)
(40,) (40, 23) [ 5 27 22 22 9 29 11 25 22 29 5 23 5 10 6 8 8 29 22 10 26 36 11 26 12 16 22 26 31 34 10 9 29 7 24 6 32 13 20 10 9 34 8 21 14 7 29 28 19 11 9 20 8 14 10 23 20 3 28 3 12 10 14 11 19 3 13 20 20 12 20 24] [19 13 25 35 13 21 10 18 17 28 15 18 7 16 10 8 10 12 25 29 14 21 12 16 11 16 13 14 9 18 15 13 18 12 11 10 30 16 14 12 12 12 30 12 12 13 17 28 11 17 9 15 11 15 16 22 18 10 17 7 18 11 12 9 15 13 8 22 17 11 16 16] (72,) (72,)
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
# cm = confusion_matrix(y_test, y_pred)
# print("Confusion Matrix:")
# print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
plot_comparison(y_test, y_pred, 'Logistic Linear Regression balanced weights, Test Set')
Accuracy: 0.05555555555555555 Correlation coefficient: 0.4046314021861102
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
# Alternatively, you can get the predicted probabilities for each class
y_prob_ = model.predict_proba(x_train)
accuracy = accuracy_score(y_train, y_pred_)
print("Accuracy:", accuracy)
# cm = confusion_matrix(y_train, y_pred_)
# print("Confusion Matrix:")
# print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
plot_comparison(y_train, y_pred_, 'Logistic Linear Regression balanced weights, Train Set')
Accuracy: 0.15862573099415206 Correlation coefficient: 0.5817856709899076
# batch download the plotted figures
# uncomment the code below to download figures if needed
'''
import glob
folder_path = '.'
# file_prefix = 'Comparison (Logistic Linear Regression Reduced Evaluation'
file_prefix = 'Comparison'
# Use glob to find all files with the given prefix in the folder
matching_files = glob.glob(f"{folder_path}/{file_prefix}*")
# print(matching_files)
# # Print the matching file names
# for file_path in matching_files:
# print(file_path)
import zipfile
zip_filename = 'files.zip'
with zipfile.ZipFile(zip_filename, 'w') as zipf:
# Add files to the zip file
for file_path in matching_files:
zipf.write(file_path)
from google.colab import files
files.download(zip_filename)
'''
Use the code cautiously.
# # Specify the path to the root folder
# root_folder = '/content'
# # Get a list of all files in the root folder
# files = os.listdir(root_folder)
# files_to_delete = [file for file in files if file.endswith(".png")]
# for file_ in files_to_delete:
# print(file_)
# # Iterate over the files and delete them
# for file in files_to_delete:
# file_path = os.path.join(root_folder, file)
# if os.path.isfile(file_path):
# os.remove(file_path)